" 4."tan^(-1)[(x)/(sqrt(a^(2)-x^(2)))]

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t. tan^(-1) ((x)/(sqrt(1-x^(2)))) .

tan^(-1)(x+sqrt(1+x^(2)))=

tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]=(pi)/(4)+(1)/(2)cos^(-1)x^(2)

y=tan^(-1)((x)/(1+sqrt(1-x^(2))))+sin(2tan^(-1)theta*sqrt((1-x)/(1+x))) then prove that ,4(1-x^(2))^(3)((d^(2)y)/(dx^(2)))^(2)+4x=x^(2)+4

int(1+tan^(2)x)/(sqrt(tan^(2)x+3))

If y = tan^(-1) {(x)/(1 + sqrt(1 - x^(2)))} + sin { 2 tan^(-1) sqrt((1 - x)/(1 + x))}, "then" (dy)/(dx) =